Question

The equation of a circle whose radius is $7$ units and $x-$coordinate of the centre is $-2$ and also touches the $x-$axis, is

• A. $x^2+y^2+4x-14y+4=0$
• B. $x^2+y^2+4x+14y+4=0$
• C. $x^2+y^2+4x-14y-49=0$
• D. $x^2+y^2+4x+14y+49=0$

Answer 1

Answer: (A), (B)

The correct options are
A $x^2+y^2+4x-14y+4=0$
B $x^2+y^2+4x+14y+4=0$

Let centre and radius of required circle are $(h,k)$ and $r$ respectively.
Given, $h=-2,r=7$
As circle touches the $x-$axis, hence $k=\pm 7$
So equation of required circle is
$(x+2{)}^2+(y-7{)}^2=7^2$
$\Rightarrow x^2+y^2+4x-14y+4=0$
And,$(x+2{)}^2+(y+7{)}^2=7^2$
$\Rightarrow x^2+y^2+4x+14y+4=0$